Smooth measures and capacities associated with nonlocal parabolic operators View Full Text


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Article Info

DATE

2019-03-27

AUTHORS

Tomasz Klimsiak, Andrzej Rozkosz

ABSTRACT

We consider a family {Lt,t∈[0,T]} of closed operators generated by a family of regular (non-symmetric) Dirichlet forms {(B(t),V),t∈[0,T]} on L2(E;m). We show that a bounded (signed) measure μ on (0,T)×E is smooth, i.e. charges no set of zero parabolic capacity associated with ∂∂t+Lt, if and only if μ is of the form μ=f·m1+g1+∂tg2 with f∈L1((0,T)×E;dt⊗m), g1∈L2(0,T;V′), g2∈L2(0,T;V). We apply this decomposition to the study of the structure of additive functionals in the Revuz correspondence with smooth measures. As a by-product, we also give some existence and uniqueness results for solutions of semilinear equations involving the operator ∂∂t+Lt and a functional from the dual W′ of the space W={u∈L2(0,T;V):∂tu∈L2(0,T;V′)} on the right-hand side of the equation. More... »

PAGES

1-44

References to SciGraph publications

Journal

TITLE

Journal of Evolution Equations

ISSUE

N/A

VOLUME

N/A

Author Affiliations

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    http://scigraph.springernature.com/pub.10.1007/s00028-019-00500-0

    DOI

    http://dx.doi.org/10.1007/s00028-019-00500-0

    DIMENSIONS

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